if the price is the main concern the fz62 should be a good option. i think the main difference between the two is the reach or the zoom capability. with the p510 a 42x zoom (which is ridiculous) if you like to shoot subjects far away, then get the p510. but if you want a decent all rounder with a good price to start the fz-62.

though if you like to experiment more with your photos, one with a hotshoe might come in handy

its expensive though but try looking for its older brothers the fz100 and the fz150 and see what youll get and how much. these have hotshoes btw which is great if you want to add versatility in the package.

but if im going with the selections you have Fz-62 since its cheaper plus I dont really find the super zoom range of the p510 useful. that is of course basing on my needs. which is the most important thing to consider

oh btw since most of your options are superzooms, take a look at the fuji hs10,20,30 the hs10 is around or les than your specified price and offers a compelling list of features. its listed as one of the best here in DP which is of course worth noting.